card distribution

Hello everyone.

This is my first post here and allow me to first say I am not a big expert on statistics so it's help what I am looking for here :)

Here the problem:

I have 15 cards and 5 players. Each player receives 3 cards, and for me it's not important in which order.

In how many ways can these be distributed?

Online I found that I should apply this formula: n! / (k!·(n - k)!)

so that with n =15 and k = 5 result is 3003.

However my doubt is, why it is not C(15,3)*C(12,3)*C(9,3)*C(6,3)*C(3,3) = 168,168,000 ?

Thanks in advance to anyone that can help
I might have misunderstood the scope of the n! / (k!·(n - k)!) - I think this was meant for establishing

how many combinations (without repeating them) of 15 cards in groups of 3 cards I can create?

but this won't help cause indeed it's important who get what.